- Tytuł:
- On infinite uniquely partitionable graphs and graph properties of finite character
- Autorzy:
-
Bucko, Jozef
Mihók, Peter - Powiązania:
- https://bibliotekanauki.pl/articles/743160.pdf
- Data publikacji:
- 2009
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
graph property of finite character
reducibility
uniquely partitionable graphs
weakly universal graph - Opis:
- A graph property is any nonempty isomorphism-closed class of simple (finite or infinite) graphs. A graph property is of finite character if a graph G has a property if and only if every finite induced subgraph of G has a property . Let ₁,₂,...,ₙ be graph properties of finite character, a graph G is said to be (uniquely) (₁, ₂, ...,ₙ)-partitionable if there is an (exactly one) partition {V₁, V₂, ..., Vₙ} of V(G) such that $G[V_i] ∈ _i$ for i = 1,2,...,n. Let us denote by ℜ = ₁ ∘ ₂ ∘ ... ∘ ₙ the class of all (₁,₂,...,ₙ)-partitionable graphs. A property ℜ = ₁ ∘ ₂ ∘ ... ∘ ₙ, n ≥ 2 is said to be reducible. We prove that any reducible additive graph property ℜ of finite character has a uniquely (₁, ₂, ...,ₙ)-partitionable countable generating graph. We also prove that for a reducible additive hereditary graph property ℜ of finite character there exists a weakly universal countable graph if and only if each property $_i$ has a weakly universal graph.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2009, 29, 2; 241-251
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł